Category:Polyominoes

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Main category: Polyforms

A polyomino is a polyform with the square as its base form. It is a connected shape formed as the union of one or more identical squares in distinct locations on the plane, taken from the regular square tiling, such that every square can be connected to every other square through a sequence of shared edges (i.e., shapes connected only through shared corners of squares are not permitted).

n Subcategory Number of free polyominoes Number of free polyominoes with holes Number of one-sided polyominoes A_n = number of fixed polyominoes
1 Monominoes 1 0 1 1
2 Dominoes 1 0 1 2
3 Trominoes 2 0 2 6
4 Tetrominoes 5 0 7 19
5 Pentominoes 12 0 18 63
6 Hexominoes 35 0 60 216
7 Heptominoes 108 1 196 760
8 Octominoes 369 6 704 2,725
9 Nonominoes 1,285 37 2,500 9,910
10 Decominoes 4,655 195 9,189 36,446
11 Undecominoes 17,073 979 33,896 135,268
12 Dodecominoes 63,600 4,663 126,759 505,861

Subcategories

This category has the following 11 subcategories, out of 11 total.

 

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Pages in category "Polyominoes"

The following 2 pages are in this category, out of 2 total.